A generalized precision matrix for non-Gaussian multivariate distributions with applications to portfolio optimization
34 Pages Posted: 6 Apr 2022 Last revised: 25 Oct 2023
Date Written: October 19, 2023
Abstract
We introduce the concept of Generalized Precision Matrix (GPM), based on a general measure of dependence, which might be valid for any statistical distribution. Beside showing that in the Gaussian case, the GPM coincides with the inverse of the covariance matrix, we derive the GPM analytically for the multivariate t, multivariate skew-normal and multivariate skew-t distributions, moving beyond Gaussianity.
Therefore, we argue that using the derived GPMs might be preferable when data show asymmetry and heavy tails, supporting our claim through simulation analysis. As financial times series are leptokurtic, we propose then an application to the Markowitz minimum variance portfolio, which exhibits superior fitting of the multivariate skew-t model during crisis periods.
Keywords: Generalized Precision Matrix, heavy tails, multivariate t distribution, multivariate skew-normal and skew-t distributions, minimum-variance portfolio
JEL Classification: C46, C58, G11
Suggested Citation: Suggested Citation